Transient Response of Gas-to-Gas Crossflow Heat Exchangers With Neither Gas Mixed

1983 ◽  
Vol 105 (3) ◽  
pp. 563-570 ◽  
Author(s):  
F. E. Romie
Keyword(s):  
Heat Exchangers ◽  
Rate Ratio ◽  
Graphical Form ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Unit Step ◽  
The Laplace Transform ◽  
Mixed Mean ◽  
Conductance Ratio ◽  
Temperature Responses

The transient mixed mean temperatures of the two gases leaving a crossflow heat exchanger are found for a unit step increase in the entrance temperature of either gas. The temperature responses are given in graphical form for the range of parameters: Ntu from 1 to 8, capacity rate ratio from 0.6 to 1.67, and conductance, ratio from 0.5 to 2.0. The solutions are found using the Laplace transform method and apply to single-pass crossflow exchangers with neither gas mixed.

Two-Dimensional Transient Solutions for Crossflow Heat Exchangers With Neither Gas Mixed

1987 ◽  
Vol 109 (2) ◽  
pp. 281-286 ◽  
Author(s):  
G. Spiga ◽  
M. Spiga
Keyword(s):  
Heat Exchangers ◽  
Initial Conditions ◽  
Transient Behavior ◽  
Computational Time ◽  
Two Dimensional ◽  
Transform Method ◽  
Wide Range ◽  
The Laplace Transform ◽  
Inlet Conditions ◽  
Conductance Ratio

The two-dimensional transient behavior of gas-to-gas crossflow heat exchangers is investigated, solving by analytical methods the thermal balance equations in order to determine the transient distribution of temperatures in the core wall and in both the unmixed gases. Assuming large wall capacitance, the general solutions are deduced by the Laplace transform method and are presented as integrals of modified Bessel functions on space and time, for a transient response with any arbitrary initial and inlet conditions, in terms of the number of transfer units, capacity rate and conductance ratio. Specializing the entrance temperature and assuming constant initial conditions, the most meaningful transient conditions (such as step, ramp, and exponential responses) have been simulated and the relevant solutions, expressed by means of either integrals or series, have been accurately computed with extremely low computational time. The temperature responses are then presented in graphic form for a wide range of the number of transfer units.

Analytical Solution of Transient Response of Gas-to-Gas Parallel and Counterflow Heat Exchangers

1987 ◽  
Vol 109 (4) ◽  
pp. 848-855 ◽  
Author(s):  
D. D. Gvozdenac
Keyword(s):  
Transient Response ◽  
Heat Exchangers ◽  
Special Functions ◽  
Dynamic Responses ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Independent Variables ◽  
The Laplace Transform

This paper shows how the transient response of gas-to-gas parallel and counterflow heat exchangers may be calculated by an analytical method. Making the usual idealizations for analysis of dynamic responses of heat exchangers, the problem of finding the temperature distributions of both fluids and the separating wall as well as the outlet temperatures of fluids is reduced to the solution of an integral equation. This equation contains an unknown function depending on two independent variables, space and time. The solution is found by using the method of successive approximations, the Laplace transform method, and special functions defined in this paper.

Dynamic Rate Effects on Timoshenko Beam Response

1985 ◽  
Vol 52 (2) ◽  
pp. 439-445 ◽  
Author(s):  
T. J. Ross
Keyword(s):  
Timoshenko Beam ◽  
Bending Moment ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Rate Effects ◽  
The Laplace Transform ◽  
Step Loading ◽  
Fixed End ◽  
Constitutive Formulation ◽  
Viscoelastic Timoshenko Beam

The problem of a viscoelastic Timoshenko beam subjected to a transversely applied step-loading is solved using the Laplace transform method. It is established that the support shear force is amplified more than the support bending moment for a fixed-end beam when strain rate influences are accounted for implicitly in the viscoelastic constitutive formulation.

scholarly journals Mathematical modeling and algorithm for calculation of thermocatalytic process of producing nanomaterial

2021 ◽  
Vol 23 (3) ◽  
pp. 1590
Author(s):  
Bakhtiyar Ismailov ◽  
Zhanat Umarova ◽  
Khairulla Ismailov ◽  
Aibarsha Dosmakanbetova ◽  
Saule Meldebekova
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Solid Phase ◽  
Nonlinear Effects ◽  
Operating Characteristics ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Wide Range ◽  
The Laplace Transform ◽  
Complex Mathematical Model

<p>At present, when constructing a mathematical description of the pyrolysis reactor, partial differential equations for the components of the gas phase and the catalyst phase are used. In the well-known works on modeling pyrolysis, the obtained models are applicable only for a narrow range of changes in the process parameters, the geometric dimensions are considered constant. The article poses the task of creating a complex mathematical model with additional terms, taking into account nonlinear effects, where the geometric dimensions of the apparatus and operating characteristics vary over a wide range. An analytical method has been developed for the implementation of a mathematical model of catalytic pyrolysis of methane for the production of nanomaterials in a continuous mode. The differential equation for gaseous components with initial and boundary conditions of the third type is reduced to a dimensionless form with a small value of the peclet criterion with a form factor. It is shown that the laplace transform method is mainly suitable for this case, which is applicable both for differential equations for solid-phase components and calculation in a periodic mode. The adequacy of the model results with the known experimental data is checked.</p>

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